%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : REL005+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:23:50 AM UTC 2026
% Result : Theorem 5.39s 3.58s
% Output : Refutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 14
% Syntax : Number of formulae : 30 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 32 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 244 ( 2 ~; 0 |; 3 &; 239 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 56 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(join_decl,type,
join: $i > $i > $i ).
thf(converse_decl,type,
converse: $i > $i ).
thf(meet_decl,type,
meet: $i > $i > $i ).
thf(complement_decl,type,
complement: $i > $i ).
thf(composition_decl,type,
composition: $i > $i > $i ).
thf(one_decl,type,
one: $i ).
thf(top_decl,type,
top: $i ).
thf(zero_decl,type,
zero: $i ).
thf(15,axiom,
! [A: $i] :
( zero
= ( A @ complement @ ( A @ meet ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero) ).
thf(56,plain,
! [A: $i] :
( zero
= ( A @ complement @ ( A @ meet ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ join ) @ composition ) )
= ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity) ).
thf(38,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ join ) @ composition ) )
= ( C @ ( B @ composition ) @ ( C @ ( A @ composition ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i] :
( top
= ( A @ complement @ ( A @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top) ).
thf(53,plain,
! [A: $i] :
( top
= ( A @ complement @ ( A @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence) ).
thf(41,plain,
! [A: $i] :
( ( A @ converse @ converse )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ composition ) @ ( A @ composition ) )
= ( C @ ( B @ ( A @ composition ) @ composition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ composition ) @ ( A @ composition ) )
= ( C @ ( B @ ( A @ composition ) @ composition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) @ converse )
= ( B @ converse @ ( A @ converse @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) @ converse )
= ( B @ converse @ ( A @ converse @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity) ).
thf(35,plain,
! [A: $i] :
( ( one @ ( A @ composition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ composition ) @ converse )
= ( A @ converse @ ( B @ converse @ composition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ composition ) @ converse )
= ( A @ converse @ ( B @ converse @ composition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
thf(20,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ join ) )
= ( A @ ( B @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet) ).
thf(29,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ meet ) )
= ( B @ complement @ ( A @ complement @ join ) @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ complement @ ( B @ ( A @ composition ) @ complement @ ( A @ converse @ composition ) @ join ) )
= ( B @ complement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( B @ complement @ ( B @ ( A @ composition ) @ complement @ ( A @ converse @ composition ) @ join ) )
= ( B @ complement ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ ( A @ meet ) @ converse @ ( B @ converse @ ( A @ converse @ meet ) @ join ) )
= ( B @ ( A @ meet ) @ converse ) )
& ( ( B @ converse @ ( A @ converse @ meet ) @ ( B @ ( A @ meet ) @ converse @ join ) )
= ( B @ converse @ ( A @ converse @ meet ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ meet ) @ converse @ ( B @ converse @ ( A @ converse @ meet ) @ join ) )
= ( B @ ( A @ meet ) @ converse ) )
& ( ( B @ converse @ ( A @ converse @ meet ) @ ( B @ ( A @ meet ) @ converse @ join ) )
= ( B @ converse @ ( A @ converse @ meet ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ meet ) @ converse @ ( B @ converse @ ( A @ converse @ meet ) @ join ) )
= ( B @ ( A @ meet ) @ converse ) )
& ( ( B @ converse @ ( A @ converse @ meet ) @ ( B @ ( A @ meet ) @ converse @ join ) )
= ( B @ converse @ ( A @ converse @ meet ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( A
= ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
thf(26,plain,
! [A: $i,B: $i] :
( A
= ( B @ ( A @ complement @ join ) @ complement @ ( B @ complement @ ( A @ complement @ join ) @ complement @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ join ) @ ( A @ join ) )
= ( C @ ( B @ ( A @ join ) @ join ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity) ).
thf(23,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ join ) @ ( A @ join ) )
= ( C @ ( B @ ( A @ join ) @ join ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(138,plain,
$false,
inference(e,[status(thm)],[56,38,53,41,32,44,35,47,20,29,50,16,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL005+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n008.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 05:25:40 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.83/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.23 % [INFO] Parsing done (220ms).
% 1.26/1.25 % [INFO] Running in sequential loop mode.
% 1.90/1.71 % [INFO] eprover registered as external prover.
% 1.90/1.72 % [INFO] Scanning for conjecture ...
% 2.06/1.83 % [INFO] Found a conjecture (or negated_conjecture) and 13 axioms. Running axiom selection ...
% 2.06/1.88 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.21/1.92 % [INFO] Problem is first-order (TPTP FOF).
% 2.21/1.93 % [INFO] Type checking passed.
% 2.21/1.93 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.39/3.56 % External prover 'e' found a proof!
% 5.39/3.57 % [INFO] Killing All external provers ...
% 5.39/3.57 % Time passed: 3010ms (effective reasoning time: 2308ms)
% 5.39/3.57 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.39/3.57 % Axioms used in derivation (13): converse_cancellativity, composition_identity, converse_idempotence, composition_associativity, maddux3_a_kind_of_de_Morgan, maddux2_join_associativity, maddux1_join_commutativity, converse_multiplicativity, converse_additivity, def_top, def_zero, composition_distributivity, maddux4_definiton_of_meet
% 5.39/3.57 % No. of inferences in proof: 30
% 5.39/3.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3010 ms resp. 2308 ms w/o parsing
% 5.60/3.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.60/3.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------